It depends what you want to do with the signal. I.e. do you just want to detect whether there is a sound or not, or do you want to analyse the sound signal in some way? It's hard to tell you what is best without making assumptions about what you are trying to do, which may be wrong.
You can think of a comparator as a 1-bit ADC. It converts an analog signal into either a logic 0 or logic 1 depending on the relative voltages of the signals on its + and - inputs. So if your sound sensor produces an AC voltage, that voltage will vary around some DC voltage, maybe 0V. If you feed the output of the sound sensor into one input of the comparator and apply 0V to the other input, then the output of the comparator will be a stream of logic 0s and 1s. That would tell you that there is a sound there and give you some information about its frequency, but none about its amplitude.
An ADC would be better if you want to have more information about the signal, such as its amplitude and waveform. Note that you will have to match the signal level of the sound sensor output to the input range of the ADC. It's no good having a signal level of 1mV and putting it into an ADC with a full-scale range of 5V.
Also note that the parallel port is only 8 bits wide, so you will be limited to using an 8-bit ADC, unless you use a serially-addressed device and "bit-bang" some of the port pins, which is quite a complex programming task.
If you just want to get a sound signal into the PC where your program can access it, why not just use the audio input jack? Just about every PC has a good quality stereo 16-bit ADC for digitising sound signals.